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Topic · Statistics and Probability

Markov Chains and Monte Carlo Methods

Markov Chains and Monte Carlo Methods is a research topic within Statistics and Probability. Science Explorer counts 12k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the application of Bayesian Monte Carlo methods, such as Markov Chain Monte Carlo (MCMC), Approximate Bayesian Computation, and Hamiltonian Monte Carlo, in scientific inference for inverse problems, model selection, and statistical estimation. It also explores adaptive MCMC algorithms and stochastic gradient Langevin dynamics for efficient parameter inference and approximation algorithms.

  • Bayesian Monte Carlo
  • Markov Chain
  • Approximate Bayesian Computation
  • Adaptive MCMC
  • Hamiltonian Monte Carlo
  • Stochastic Gradient Langevin Dynamics
  • Inverse Problems
  • Model Selection
  • Statistical Inference
  • Approximation Algorithms
Research works
12k
fractional, since 1950
In the world top 10%
1.2k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+20%
the tick is no change
Largest producer
United States
35% of the 10 largest, 2022-now
Markov Chains and Monte Carlo Methods

Which countries lead Markov Chains and Monte Carlo Methods research?

By volume, the United States and France publish the most (566 and 220 works in 2022-now).

By volume, 2022-now

  1. 1 United States 566 works
  2. 2 France 220 works
  3. 3 China 212 works
  4. 4 United Kingdom 167 works
  5. 5 Germany 138 works
  6. 6 Italy 77 works
  7. 7 Japan 73 works
  8. 8 Canada 65 works
  9. 9 Russia 47 works
  10. 10 India 47 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 35.1%France: 13.7%China: 13.1%United Kingdom: 10.4%6 others listed: 27.7%35%largest
United States566 · 35.1%France220 · 13.7%China212 · 13.1%United Kingdom167 · 10.4%6 others listed447 · 27.7%

Shares of the rows listed above, not of the whole node.

Which institutions lead Markov Chains and Monte Carlo Methods research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Markov Chains and Monte Carlo Methods research, followed by Stanford University and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 90 works
  2. 2 Stanford UniversityUnited States 21 works
  3. 3 Russian Academy of SciencesRussia 19 works
  4. 4 University of WarwickUnited Kingdom 19 works
  5. 5 University of CambridgeUnited Kingdom 17 works
  6. 6 New York UniversityUnited States 17 works
  7. 7 Georgia Institute of TechnologyUnited States 16 works
  8. 8 Columbia UniversityUnited States 15 works
  9. 9 Massachusetts Institute of TechnologyUnited States 15 works
  10. 10 University of California, BerkeleyUnited States 14 works

Who are the leading researchers in Markov Chains and Monte Carlo Methods?

The most-cited researchers publishing on Markov Chains and Monte Carlo Methods include Yoshua Bengio, Geoffrey E. Hinton and Karl John Friston.

  1. 1 Yoshua Bengio Canada 476k citations
  2. 2 Geoffrey E. Hinton Canada 454k citations
  3. 3 Karl John Friston United Kingdom 310k citations
  4. 4 Trevor Hastie United States 301k citations
  5. 5 Richard A. Gibbs United States 292k citations
  6. 6 Xiaogang Wang China 260k citations
  7. 7 Leo Breiman United States 243k citations
  8. 8 Harry Eugene Stanley United States 198k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Markov Chains and Monte Carlo Methods?

The most cited paper in Markov Chains and Monte Carlo Methods is "Monte Carlo sampling methods using Markov chains and their applications" (W. Keith Hastings, 1970), with 15,456 citations. Next come "emcee : The MCMC Hammer" (12,323) and "General Methods for Monitoring Convergence of Iterative Simulations" (6,193).

Most cited papers
#PaperReleasedCitations
1 Monte Carlo sampling methods using Markov chains and their applications W. Keith Hastings · Biometrika Apr 1970 15,456
2 emcee : The MCMC Hammer Daniel Foreman-Mackey, David W. Hogg, Dustin Lang et al. · Publications of the Astronomical Society of the Pacific Open access Mar 2013 12,323
3 General Methods for Monitoring Convergence of Iterative Simulations Stephen P. Brooks, Andrew Gelman · Journal of Computational and Graphical Statistics Dec 1998 6,193
4 Reversible jump Markov chain Monte Carlo computation and Bayesian model determination Peter J. Green · Biometrika 1995 5,963
5 Monte Carlo Statistical Methods Hoon Kim, Christian P. Robert, George Casella · Technometrics Open access Nov 2000 5,603
All 100 most cited papers, with filters and sorting

Where is Markov Chains and Monte Carlo Methods research done?

The largest centres of Markov Chains and Monte Carlo Methods research in 2022-now are Paris (France), Beijing (China), New York (United States) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Stanford.

Largest cities, 2022-now

  1. 1 ParisFrance 86 works
  2. 2 BeijingChina 49 works
  3. 3 New YorkUnited States 38 works
  4. 4 TokyoJapan 38 works
  5. 5 LondonUnited Kingdom 38 works
  6. 6 MoscowRussia 27 works
  7. 7 ShanghaiChina 22 works
  8. 8 CambridgeUnited States 21 works
  9. 9 StanfordUnited States 21 works
  10. 10 RomeItaly 20 works

Where it is the local speciality

  1. StanfordUS · 21.0 works7.4×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Markov Chains and Monte Carlo Methods than the world average.

See Markov Chains and Monte Carlo Methods on the map

Where is the best place to study Markov Chains and Monte Carlo Methods?

Among universities, judged by research, Université Paris Sciences et Lettres, Massachusetts Institute of Technology and ETH Zurich score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%mean 16.25%fractional works in this field (log) →share of work in the world top 10% →ETH ZurichMassachusetts Instit…Université Paris Sci…New York University
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Université Paris Sciences et LettresFrance 78.018.7%19.8×13 +19.6%
2Massachusetts Institute of TechnologyUnited States 72.220.7%12.2×15 -20.1%
3ETH ZurichSwitzerland 71.822.6%10.0×12 -27.0%
4New York UniversityUnited States 70.912.3%8.5×17 +31.8%
5University of WarwickUnited Kingdom 70.39.7%23.0×19 +27.3%
6University of EdinburghUnited Kingdom 69.516.4%7.5×12 +31.4%
7Stanford UniversityUnited States 68.213.8%8.0×21 -10.7%
8National University of SingaporeSingapore 66.215.4%6.0×13 +59.3%
9Columbia UniversityUnited States 64.116.4%7.8×15 +68.4%
10Imperial College LondonUnited Kingdom 60.816.5%6.2×11 +47.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Markov Chains and Monte Carlo Methods, country by country

Is Markov Chains and Monte Carlo Methods research growing?

Output in 2022-2025 was 20% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Markov Chains and Monte Carlo Methods.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Markov Chains and Monte Carlo Methods as a percentage of every work published that year, 0.0067% in 2024.

still counting0.010%0.020%0.030%Markov Chains and Monte Carlo Methods0.0077% in 202519801990200020102020

Fractional works of Markov Chains and Monte Carlo Methods over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Markov Chains and Monte Carlo Methods10.1% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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